IMHO, the answer is no...not in the current version of Karma. I can offer my thoughts, but bear in mind I don't really know what I'm talking about.
I think follow-me depends as much on software as it does on hardware.
In terms of software, there would need to be an update to the Hero cameras (4B/5B/5S) and to the controller to allow you to define who (or what) exactly you're following. I doubt the current line has the processing capacity to take on that additional burden (just look at how slow the simulator is on the Karma controller). The best hope would be the Hero6 when it comes out later this year; perhaps it might bring new features to Karma? Time will tell.
The hardware also isn't really in a position to support follow-me. Again, this is only my opinion, but follow-me is pretty useless without obstacle avoidance to ensure that the drone doesn't fly straight into something while it's following you. In turn, obstacle avoidance that isn't perfect is a bit gimmicky; I just wouldn't want to trust it unless I was very sure that it would be foolproof, and the DJI implementations of obstacle avoidance don't work at high speed nor can they see small objects such as branches (or wire fences). So if you can't trust the obstacle avoidance, would you really want to take your hands off the controller and your eyes off the drone and just let it follow you?
Given that GoPro have a consumer-oriented customer base (as opposed to DJI's more enthusiast-oriented base), they're more likely to have complaints from customers that "it didn't work perfectly out of the box". I think they predicted that it would just too much pain for them to have it in version 1.0, and opted to reduce their costs by building hardware that can't support follow-me/obstacle avoidance.
Having said that, there have been so many complaints that it's not in Karma that I suspect GoPro will succumb to the pressure and add it in v2.0 (who knows when that will be), but I'm still not sure I'd want to trust it.
Just my $0.02 worth.